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The medicinal thermometer commonly used in homes can be read $\pm 0.1^{\circ} \mathrm{F},$ whereas those in the doctor's office may be accurate to $\pm 0.1^{\circ} \mathrm{C} .$ In degrees Celsius, express the percent error expected from each of these thermometers in measuring a person's body temperature of $38.9^{\circ} \mathrm{C}.$

$$102.02^{\circ} \mathrm{F}$$

Chemistry 101

Chapter 1

Chemistry: The Study of Change

Intro to Chemistry

University of Central Florida

Drexel University

Brown University

Lectures

02:29

Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry deals with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds. Chemistry also involves understanding the properties and interactions of individual atoms and molecules for use in larger-scale applications.

04:42

In chemistry and physics, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic particles, and in everyday as well as scientific usage, "matter" generally includes atoms and anything made up of them, and any particles and objects that act as if they have both rest mass and volume. However it does not include massless particles such as photons, or other energy phenomena or waves such as light or sound. Matter exists in various states (known as phases) that are defined by various physical properties, such as state of matter, phase, shape, and density. The Standard Model of particle physics and the general theory of relativity describe fundamental particles and the fundamental forces acting between them that control the structure and dynamics of matter.

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The medicinal thermometer …

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So this question is a percent error calculation question. So they give you the air associated with medicinal thermometers using homes just 0.1 degrees Fahrenheit. And then they give you the air associated with, um, thermometers using the doctor's office, which is 0.1 degrees Celsius. And they want you to calculate the person error with respect to a person body temperature, who is 38.9 degrees Celsius. So we're gonna have to cut do 2%. Eric calculations here, one for fair and high and one for Celsius. We're one for them home and then one for the doctor's office. So first we have to do is convert the body temperature of 38.9 degrees Celsius to Fahrenheit so that we can do the calculation much easier. Um, so it's straight out our degrees Fahrenheit two or three Celsius degrees Fahrenheit. Formula 2 F equals 9/5 degrees Celsius. Whatever number that is, plus 32 and you plug in 38.9. You should get 102 0.2 degrees. Sure enough. Okay, that's our value right here. Now let's go Over. What percent error is um, so percent airline you're out of the equation. Percent here is equal to the absolute value of the actual observe ice of V A minus the expected value ve over the expected value again Be okay. I'm gonna do this times 100% because we want to get a percentage here. So basically, um, percent error is the percentage off of your expected value that your actual value was. So how off is your actual value from your expected value? So if it's a high percent error than you know, your expected, your actual value is very different from your expected value. Okay, so we basically have all the information we need for this because they give you the error. Okay, So, um, they give you the air already, which is, like 0.1 degrees Fahrenheit and then 0.1 degrees Celsius so that actually the this whole part top part of this equation actual minus expected is just the error is what they've given us already, because that is how much it's going to deviate, right? The medicinal dominant thermometer in like Holmes is accurate to zero toe plus minus 0.1 degrees Fahrenheit. So that's how much will deviate from the actual value so we can just plug that in for our top part. We can find the percent here, so let's do the percent air of the Fahrenheit first. So I'm gonna put Fahrenheit on the side, just kind of like to make it clear. And you're gonna do what, 0.1 Fahrenheit, right degrees Fahrenheit? Because that is how much it will maximally deviate. So this is your maximum percent error here over 102.0 two. Okay, times 100%. And they should get you your foot one divided by subsequent there, too. Um, this should get you nine points. 80 times tell to the *** fourth, um, times 100%. So if you just do the 100% you should get what with the decimal point to the left. And you should get zero point zeer or to the right, 0.0 98 zero percent air. Okay, so a very, very small percent air we have here for medicinal home. Now, let's do the Celsius one. We could expect this to be decently higher because the expected value, of course, is not as large. Now we have 0.1 degrees Celsius all over 30 h 0.9 degrees Celsius. Time in 100%. It wasn't your calculator. 38 29 100. And you should get 0.2 57 percent here. Okay, so, yeah, this is made because what percent area is and how you do the calculations. Just a couple important things to remember. Just remember that the that error and general or how much of the value would deviate, which is the numbers that give us right 0.1 degrees Fahrenheit, 0.1 degree Celsius. How much the numbers will deviate is just the same as Val actual value minus the expected value. That was kind of the key thing for this question. Or the only tricky thing for this question s Oh, yeah, percent errors are very, very important in just terms of data down analysis and all sorts of chemistry and biology and just, you know, in general, experimental stuff. So I hope this is helpful. And thank you for listening

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